1. Field of the Invention
The present invention relates to a method of computing an amount of defocus in lithography and also to a lithographic process using the method. More particularly, the present invention pertains to a method of computing a defocus amount that is used as an index for the optimization of lithographic factors that affect lithographic accuracy in a lithographic process which requires formation of fine patterns, as in the case of a semiconductor process. The invention also pertains to a lithographic process which utilizes such a defocus-amount computing method.
2. Description of the Related Art
Lithographic processes which require formation of fine patterns, as in semiconductor processes, employ various devices. Such devices include an exposure device having a projection lens system, e.g., a so-called demagnification projection lens system or a real-size projection lens system, for transferring a reticle pattern onto a wafer, or an exposure device which permits writing of a pattern directly on a wafer by means of an electron beam.
Exposure relying on such an exposure device suffers from a problem in that the lithographic resolution limit is directly affected by a beam defocus that is attributable to aberrations in the lens system. Large aberrations, i.e., a large beam-defocus, a hamper-precise transfer or writing of a pattern onto a wafer, lead to degradation of the characteristics and a malfunction of the product semiconductor devices. In order to obviate this problem, it is essential to adjust the lens system by effecting, for example, optical axis alignment and aberration correction, based on the result of a quantitative detection of the aberrations.
Conventionally, a resist pattern is formed on a wafer at an arbitrary position by a lithographic process, and the line widths of the formed pattern are measured by magnifying the pattern line through an electron microscope. Aberrations and other factors are determined through a computation performed using the measured light widths, and the adjustment of the lens system is effected based on the result of the computation.
In another method, a lens system of an exposure device used in a lithographic process is adjusted in accordance with an amount of defocus calculated based on the waveforms of secondary beams and the reflected beams produced when an edge of a metallic pattern formed in a wafer is scanned with an exposure beam.
The lithographic processes employing these known exposure-device adjusting techniques, however, involve the following problems.
Namely, the first-mentioned adjusting technique relying upon the aberrations determined based on the resist pattern line widths has a drawback in that variations in the lithographic factors, i.e., changes in the characteristics of the lens system of the exposure device, are less likely to appear on the line width of the resist pattern. This leads to a problem in that the values of the aberrations determined based on the line widths tend to involve errors that are not attributable to the lens system but to other factors such as variations in the exposure rate, fluctuation of the developing conditions, temperature distributions in pre-bake and post-bake ovens, and so forth.
It is, therefore, not easy to optimize the lens system of the exposure device through an adjustment using aberrations determined by this technique.
The second-mentioned technique relying upon the scanning of a metallic pattern edge with an exposure beam can accurately determine the amount of the exposure-beam defocus attributable to the lens system. The amount of the defocus of the exposure beam determined by this technique, however, contains error factors such as a defocus caused when the beam is deflected towards the position of the metallic pattern and defocus caused by the scanning oscillation of the exposure beam. Consequently, the defocus amount determined by this technique does not exactly indicate the amount of defocus of the exposure beam alone in the lithography. Optimization of the lens system of the exposure device is therefore difficult to effect, even with the exposure-beam defocus amount determined by the second-mentioned technique.
Accordingly, it is an object of the present invention to provide a method of computing a defocus amount, as well as a lithographic process, which overcomes the above-described problems of the known arts.
To this end, according to one aspect of the present invention, there is provided a method of computing a defocus amount in lithography comprising the steps of measuring the line width and the edge roughness of a resist pattern formed by lithography and calculating, based on the measured line width and the measured edge roughness, the amount of defocus of a pseudo-profile of the beam used in the lithography.
In accordance with the invention, the defocus amount of the pseudo-profile of the beam is calculated based on the line width and the edge roughness of the resist pattern. The term xe2x80x9cpseudo-profile of the beamxe2x80x9d is used here to mean a pseudo-form of the beam profile, i.e., the pseudo-beam intensity distribution, which contains defocus components of all the lithographic factors that affect the accuracy of the lithography. As will be fully described later, FIG. 9 shows the relationship between the edge roughness and the inverse of a gradient of the pseudo-profile of the beam, i.e., the differentiated value of the pseudo-profile of the beam, that is taken at the threshold level of the profile that is the minimum level of the dosage required for resolving the resist. As will be seen from FIG. 9, the edge roughness is in proportion to the inverse of the gradient of the pseudo-profile of the beam, i.e., the inverse of the differentiated value of the profile, which well indicates the amount of variation. For these reasons, the amount of defocus calculated based on the edge roughness provides an index which sensitively indicates the rate of variation of the gradient of the pseudo-profile of the beam and, hence, the change in a lithographic factor or factors which affect the pseudo-profile of the beam.
In accordance with another aspect of the present invention, there is provided a lithographic process which, based on the amount of defocus computed through the described method, optimizes a lithographic factor that causes the defocus of the pseudo-beam profile.
In the lithographic process of the present invention, the lithographic factor is optimized based on the amount of defocus of the pseudo profile of the beam which sensitively reflects a change in the lithographic factor, thus ensuring better optimization of the lithographic factor.